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SUMMARY:Potential new pathways in modelling sea ice phenomena coming from 
 the analysis of multiscale solids with defects - Michael Nieves (Keele Uni
 versity\; University of Cagliari\; University of Liverpool)
DTSTART:20171206T153000Z
DTEND:20171206T163000Z
UID:TALK96604@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:In this talk\, we discuss two methods used in the modelling of
  materials with defects at different scales.  &nbsp\;  The first\, known a
 s the method of mesoscale asymptotic approximations [1]\, &nbsp\;is approp
 riate for the modelling of granular materials. In particular\, we discuss 
 the approximation of solutions to a particular class of transmission probl
 ems in solids containing clusters of many small inclusions\, which can int
 eract with each other [2]. The asymptotics are supplied with remainder est
 imates that are rigorously justified.&nbsp\;  &nbsp\;  The second method c
 oncerns the dynamic failure of structured materials\, commonly used in und
 erstanding the phenomena involved at multiple scales in the fracture of so
 lids. The subject has been explored in the last 30 years for a variety of 
 mass-spring systems [3].&nbsp\;  Here\, we take a different approach and c
 onsider faults propagating through periodic mass-beam systems [4\, 5]\, wh
 ich are more commonly found in civil engineering applications such as long
  rooftops\, bridges and pipeline systems. We give a summary of analytical 
 results\, based on the Fourier transform and the Wiener-Hopf technique\, c
 oncerning the dynamic behaviour of the structure during the failure.  &nbs
 p\;  Numerical simulations demonstrate the effectiveness of both approache
 s.  It is envisaged that both techniques may find a new home in the modell
 ing of phenomena associated with the behaviour of sea ice.  &nbsp\;  <span
 ><b>References:</b>&nbsp\;</span>  [1] V. Maz&rsquo\;ya\, A. Movchan and M
 . Nieves\, (2013): Green&rsquo\;s Kernels and Meso-Scale Approximations in
  Perforated Domains\, Lecture Notes in Mathematics 2077\, Springer.  [2] M
 .J. Nieves\, (2017): Asymptotic analysis of solutions to transmission prob
 lems in solids with many inclusions\, SIAM J. Appl. Math. 77 (4)\, 1417-14
 43.  [3] L.I. Slepyan\, &nbsp\;(2002): Models and Phenomena in Fracture Me
 chanics\, Foundations of Engineering Mechanics\, Springer.  [4] M.J. Nieve
 s\, G.S. Mishuris\, L.I. Slepyan\, (2016): Analysis of dynamic damage prop
 agation in discrete beam structures\, Int. J. Solids Struct. 97-98\, 699-7
 13.&nbsp\;  [5] M.J. Nieves\, G.S. Mishuris\, L.I. Slepyan\, (2017): Trans
 ient wave in a transformable periodic flexural structure\, Int. J. Solids 
 Struct. 112\, 185-208<br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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